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For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?
- a)48
- b)49
- c)50
- d)51
- e)52
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
For how many integer values of n will the value of the expression 4n +...
1 < 4n + 7 < 200
n can be 0, or -1
n cannot be -2 or any other negative integer or the expression 4n + 7 will be less than1.
The largest value for n will be an integer < (200 - 7) /4
193/4 = 48.25, hence 48
The number of integers between -1 and 48 inclusive is 50
n can be 0, or -1
n cannot be -2 or any other negative integer or the expression 4n + 7 will be less than1.
The largest value for n will be an integer < (200 - 7) /4
193/4 = 48.25, hence 48
The number of integers between -1 and 48 inclusive is 50
Most Upvoted Answer
For how many integer values of n will the value of the expression 4n +...
To find the integer values of n for which the expression 4n + 7 is an integer greater than 1 and less than 200, we need to consider the range of possible values for n.
1. Upper Limit:
The expression 4n + 7 should be less than 200. So, we can write the inequality as:
4n + 7 < />
Subtracting 7 from both sides:
4n < />
Dividing both sides by 4:
n < />
2. Lower Limit:
The expression 4n + 7 should be greater than 1. So, we can write the inequality as:
4n + 7 > 1
Subtracting 7 from both sides:
4n > -6
Dividing both sides by 4:
n > -1.5
3. Combining the Inequalities:
From the upper limit, we know that n < 48.25,="" but="" since="" n="" should="" be="" an="" integer,="" the="" maximum="" possible="" value="" for="" n="" is="" />
From the lower limit, we know that n > -1.5, but since n should be an integer, the minimum possible value for n is -1.
4. Counting the Integer Values:
To find the count of integer values of n within this range, we subtract the minimum value from the maximum value and add 1:
48 - (-1) + 1 = 50
Therefore, there are 50 integer values of n for which the expression 4n + 7 is an integer greater than 1 and less than 200.
Hence, the correct answer is option C) 50.
1. Upper Limit:
The expression 4n + 7 should be less than 200. So, we can write the inequality as:
4n + 7 < />
Subtracting 7 from both sides:
4n < />
Dividing both sides by 4:
n < />
2. Lower Limit:
The expression 4n + 7 should be greater than 1. So, we can write the inequality as:
4n + 7 > 1
Subtracting 7 from both sides:
4n > -6
Dividing both sides by 4:
n > -1.5
3. Combining the Inequalities:
From the upper limit, we know that n < 48.25,="" but="" since="" n="" should="" be="" an="" integer,="" the="" maximum="" possible="" value="" for="" n="" is="" />
From the lower limit, we know that n > -1.5, but since n should be an integer, the minimum possible value for n is -1.
4. Counting the Integer Values:
To find the count of integer values of n within this range, we subtract the minimum value from the maximum value and add 1:
48 - (-1) + 1 = 50
Therefore, there are 50 integer values of n for which the expression 4n + 7 is an integer greater than 1 and less than 200.
Hence, the correct answer is option C) 50.
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For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?a)48b)49c)50d)51e)52Correct answer is option 'C'. Can you explain this answer?
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For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?a)48b)49c)50d)51e)52Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?a)48b)49c)50d)51e)52Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?a)48b)49c)50d)51e)52Correct answer is option 'C'. Can you explain this answer?.
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